Maximum size square sub-matrix with all 1s

Given a binary matrix, I have find out the maximum size square sub-matrix with all 1s.

For example, consider the below binary matrix:

   0  1  1  0  1 
   1  1  0  1  0 
   0  1  1  1  0
   1  1  1  1  0
   1  1  1  1  1
   0  0  0  0  0

The maximum square sub-matrix with all set bits is

1  1  1
1  1  1
1  1  1

I searched the web for solutions and I found a relation to construct an auxiliary matrix:

 If M[i][j] is 1 then
            S[i][j] = min(S[i][j-1], S[i-1][j], S[i-1][j-1]) + 1
         Else /*If M[i][j] is 0*/
            S[i][j] = 0

1. Where M[][] is the original matrix and s[][] is the auxiliary matrix?
2. What does this relation signify?
3. And how is it helpful.